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  <div class="section" id="numpy-random-generator-wald">
<h1>numpy.random.Generator.wald<a class="headerlink" href="#numpy-random-generator-wald" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.random.Generator.wald">
<code class="sig-prename descclassname">Generator.</code><code class="sig-name descname">wald</code><span class="sig-paren">(</span><em class="sig-param">mean</em>, <em class="sig-param">scale</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.Generator.wald" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw samples from a Wald, or inverse Gaussian, distribution.</p>
<p>As the scale approaches infinity, the distribution becomes more like a
Gaussian. Some references claim that the Wald is an inverse Gaussian
with mean equal to 1, but this is by no means universal.</p>
<p>The inverse Gaussian distribution was first studied in relationship to
Brownian motion. In 1956 M.C.K. Tweedie used the name inverse Gaussian
because there is an inverse relationship between the time to cover a
unit distance and distance covered in unit time.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>mean</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Distribution mean, must be &gt; 0.</p>
</dd>
<dt><strong>scale</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Scale parameter, must be &gt; 0.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">mean</span></code> and <code class="docutils literal notranslate"><span class="pre">scale</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(mean,</span> <span class="pre">scale).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized Wald distribution.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The probability density function for the Wald distribution is</p>
<div class="math">
<p><img src="../../../_images/math/ca1b35b5f88da786b826e117e4af8cc53d64bf2c.svg" alt="P(x;mean,scale) = \sqrt{\frac{scale}{2\pi x^3}}e^
\frac{-scale(x-mean)^2}{2\cdotp mean^2x}"/></p>
</div><p>As noted above the inverse Gaussian distribution first arise
from attempts to model Brownian motion. It is also a
competitor to the Weibull for use in reliability modeling and
modeling stock returns and interest rate processes.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="ra35a579c0a2d-1"><span class="brackets">1</span></dt>
<dd><p>Brighton Webs Ltd., Wald Distribution,
<a class="reference external" href="https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp">https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp</a></p>
</dd>
<dt class="label" id="ra35a579c0a2d-2"><span class="brackets">2</span></dt>
<dd><p>Chhikara, Raj S., and Folks, J. Leroy, “The Inverse Gaussian
Distribution: Theory : Methodology, and Applications”, CRC Press,
1988.</p>
</dd>
<dt class="label" id="ra35a579c0a2d-3"><span class="brackets">3</span></dt>
<dd><p>Wikipedia, “Inverse Gaussian distribution”
<a class="reference external" href="https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution">https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Draw values from the distribution and plot the histogram:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">h</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span><span class="o">.</span><span class="n">wald</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">100000</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-Generator-wald-1.png" src="../../../_images/numpy-random-Generator-wald-1.png" />
</div>
</dd></dl>

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